A Semiclassical, Entropic Proof of a Weak Gravity Conjecture

Abstract

We present a semiclassical proof of the weak gravity conjecture in $D=4$ spacetime dimensions for scalar matter gauged under a $U(1{)}^N$ gauge group. We compute the non-perturbative macroscopic entropy of a scalar field in an extremal black hole background at the level of linearized backreaction on the metric. The scalar field is assumed to violate or saturate the weak gravity conjecture. The scalar contributes a logarithmic correction to the entropy in the black hole geometry that outgrows the classical contribution. We demonstrate that the entropy of the gauged scalar violates the generalized second law in the limit of large black hole charge. Our result suggests that entropy inequalities may directly discriminate between effective field theories that live in the landscape versus the swampland.

v3: 25 pages, clarified main result of the paper and created section on consistency checks on main argument;v2: 25 pages, significantly expanded discussion on renormalization and backreaction to demonstrate validity of our results

References in corpus (6)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Relative entropy and the Bekenstein bound
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Infrared Consistency and the Weak Gravity Conjecture
• Proof of a Quantum Bousso Bound
• Entropy on a null surface for interacting quantum field theories and the Bousso bound